Some New Results in Differential Algebraic Control Theory

In this paper, static state and dynamic state feedback linearisation are considered in the framework of differential algebra. The relationship between dynamic feedback and FLATNESS defined by Fliess is discussed. The existence of an equivalent PROPER DIFFERENTIAL I-O SYSTEM for a given differential I-O system is discussed, which is closely related to the choice of a proper fictitious output in control design. The concept of FLATNESS and its relaxation to dynamic feedback libearisability, controlability, observability, invertibility and minimal realisation are discussed. Finally it is demonstrated that many fundamental control concepts and their interrelationships can be incorporated into an extended control diagram.